7.9.3 problem 15

Internal problem ID [251]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.2 (General solutions of linear equations). Problems at page 122
Problem number : 15
Date solved : Monday, January 27, 2025 at 02:42:56 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 15

dsolve([diff(y(x),x$3)-3*diff(y(x),x$2)+3*diff(y(x),x)-y(x)=0,y(0) = 2, D(y)(0) = 0, (D@@2)(y)(0) = 0],y(x), singsol=all)
 

\[ y = \left (x^{2}-2 x +2\right ) {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 17

DSolve[{D[y[x],{x,3}]-3*D[y[x],{x,2}]+3*D[y[x],x]-y[x]==0,{y[0]==2,Derivative[1][y][0] ==0,Derivative[2][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (x^2-2 x+2\right ) \]